Random polynomials
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Bibliographic Information
Random polynomials
（Probability and mathematical statistics : a series of monographs and textbooks）
Academic Press, 1986
- : alk.paper
- : pbk
Available at / 58 libraries
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Science and Technology Library, Kyushu University
pbkBHAR/10/K1068252186005194,
BHAR/10/4068222189001551 -
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Includes bibliographies and index
Description and Table of Contents
Description
Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Random Polynomials focuses on a comprehensive treatment of random algebraic, orthogonal, and trigonometric polynomials. The publication first offers information on the basic definitions and properties of random algebraic polynomials and random matrices. Discussions focus on Newton's formula for random algebraic polynomials, random characteristic polynomials, measurability of the zeros of a random algebraic polynomial, and random power series and random algebraic polynomials. The text then elaborates on the number and expected number of real zeros of random algebraic polynomials; number and expected number of real zeros of other random polynomials; and variance of the number of real zeros of random algebraic polynomials. Topics include the expected number of real zeros of random orthogonal polynomials and the number and expected number of real zeros of trigonometric polynomials. The book takes a look at convergence and limit theorems for random polynomials and distribution of the zeros of random algebraic polynomials, including limit theorems for random algebraic polynomials and random companion matrices and distribution of the zeros of random algebraic polynomials. The publication is a dependable reference for probabilists, statisticians, physicists, engineers, and economists.
Table of Contents
Preface
Acknowledgments
Chapter 1 Introduction
1.1 Introduction
1.2 Origins of Some Random Algebraic Polynomials
1.3 Some Historical Remarks
1.4 Other Types of Random Polynomials
References
Chapter 2 Random Algebraic Polynomials: Basic Definitions and Properties
2.1 Introduction
2.2 Random Power Series and Random Algebraic Polynomials
2.3 Other Definitions of Random Algebraic Polynomials
2.4 Measurability of the Zeros of a Random Algebraic Polynomial
2.5 Measurability of the Number of Zeros of a Random Algebraic Polynomial
2.6 Some Properties of Random Algebraic Polynomials
References
Chapter 3 Random Matrices and Random Algebraic Polynomials
3.1 Introduction
3.2 Some Examples of Random Matrices
3.3 Random Characteristic Polynomials
3.4 Newton's Formula for Random Algebraic Polynomials
3.5 Random Companion Matrices
References
Chapter 4 The Number and Expected Number of Real Zeros of Random Algebraic Polynomials
4.1 Introduction
4.2 Estimates ?n(?, ?)
4.3 The Expected Number of Real Zeros of Random Algebraic Polynomials
4.4 The Average Number of Zeros of Random Algebraic Polynomials with Complex Coefficients
References
Chapter 5 The Number and Expected Number of Real Zeros of Other Random Polynomials
5.1 Introduction
5.2 The Number and Expected Number of Real Zeros of Trigonometric Polynomials
5.3 The Expected Number of Real Zeros of Random Hyperbolic Polynomials
5.4 The Expected Number of Real Zeros of Random Orthogonal Polynomials
5.5 Numerical Results
References
Chapter 6 The Variance of the Number of Real Zeros of Random Algebraic Polynomials
6.1 Introduction
6.2 The Main Theorem
6.3 Formula for the Variance
6.4 Some Lemmas
6.5 Proof of Theorem 6.2(a)
6.6 Proof of Theorem 6.2(b)
6.7 Some Computational Results
References
Chapter 7 Distributions of the Zeros of Random Algebraic Polynomials
7.1 Introduction
7.2 Distribution of the Real Zeros of Random Linear and Quadratic Equations
7.3 Distribution of the Zeros of a Random Polynomial with Complex Coefficients
7.4 Condensed Distribution of the Zeros of a Random Algebraic Polynomial
7.5 Distribution of the Number of Real Zeros
7.6 Some Numerical Results
7.7 On the Distribution of the Zeros of Random Algebraic Polynomials
References
Chapter 8 Convergence and Limit Theorems for Random Polynomials
8.1 Introduction
8.2 The Limiting Behavior of n-1Nn (B, ?)
8.3 The Limiting Behavior of Fn,k(z, ?) and Nn,k(B, ?)
8.4 Stability of the Zeros of Random Algebraic Polynomials
8.5 Some Limit Theorems for Random Algebraic Polynomials and Random Companion Matrices
References
Appendix Fortran Programs
Index
by "Nielsen BookData"
